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I wanted to point out to you guys the discussion about perfect 12ths tuning on the CAUT list. Really it is about the new tuning program you can get on your I-phone. It uses Bernhard Stoppers program and theories of perfect 12th tuning. Kent Swafford posted a mp3 of two pianos tuned together using Pure Tone (I think that's the name) Remarkably good and the tunings are considered high quality. He tuned a Bosey Imperial and a S&S D.

The amazing thing is, the program uses no memory. It doesn't matter whether you tune one note on one piano and then one on another. Order of notes tuned makes absolutly no difference.

Originally posted by Keith Roberts:The amazing thing is, the program uses no memory. It doesn't matter whether you tune one note on one piano and then one on another. Order of notes tuned makes absolutly no difference.

Computer programs use memory, period.

Perhaps you meant this one uses a different approach, where the whole tuning is not calculated before starting to adjust the tension, or something like that?

The original mp3 file seems to be gone, do you still have it? If so, could you please upload it somewhere for those of us who didn't manage to get it?

This is very interesting (in both computational and tuning matters). Thanks for posting this here

Stopper's taking a beating in the iPhone app store review section. The so-called "Tunic Guitar" goes for Free (A=430Hz), lite for $25 and the full for $60. I remember the piano one going for $600+, but I didnt see that in iPhone yet.

So if the piano is $600, and you get 88 notes, for $6.82 per note. On guitar, you have the five notes there, so that would make $34.09. The lite seems like it is a deal at an almost 9 dollar savings.

The lite doesn't have the ability to adjust its scales though. The pointy interface doesn't seem eye-pleasing as he describes it in the store, although it's great for accuracy and visibility.

I heard Stopper's tuning at the National in June. I must say I was blown away.

He played an octave - it sounded fine, nice and clean. Then he played the tonic- fifth interval and the fifth - octave interval. They sounded good - a nice, slow roll. Then he played the tonic - fifth - octave. It was absolutely pure and clean! The beats canceled each other out. It was amazing.

When playing big chords with both hands, any key: after the initial attack, the chord just stood there in the room, solid and clean, it sounded like a church organ.

You can calculate octave stretch and inharmonicity all you want - when the sounds makes the hair on the back of your neck stand on end, you know something good is going on.

Forgive me for being a "party pooper" on this one guys. I'll probably take some heat for these comments, but I listened to these mp3 files (repeatedly). And I dont hear what you guys seem to be hearing.

First let me say I am not a fan of recorded piano music. Getting a good recording of a piano by itself, is a highly artistic thing, and few people achieve it with a high degree of success. I tolerate a piano with an orchestra or other instruments much better.

I think the tuning on the Bosie and the D were better than on the Everett Spinet (of course).I was for the most part with you guys during the first 5 to 10 seconds of the recording, then to me it kind of falls apart. Listen to those unisons, especially in the upper end. Not good.Listen to the Octaves being played together. They make my skin crawl. Very dirty like badly tuned fifths.

Overall I personally dont believe these recording are examples of excellent piano tuning.

I have to say that I agree with Ron. Like he said, maybe it's the way the recording came across but, personally, I doubt that. It's the same on all of the tunings although, worse on the Everett. I heard out of tune unison's especially up in the higher treble area.

I didn't like the way the lower bass sounded either. I thought it was to sharp.

The further up he went, the flatter the octaves were in comparison to the mid range and lower notes, they weren't stretched. When playing 4 octaves together, it sounded pretty bad to me.

If you noticed, on every test, the further he went up, the faster he played it. People usually do that so that you can't hear it as well but, I could still pick it out. So, over all, while it was probably "ok" or, so he thought, it wasn't good enough to suit me. I wouldn't use a tuning that sounded like that in the end. Maybe too, it was the tuner not familiar enough with the tuning, I don't know but, I do know that I wasn't satisfied with the tuning overall.

Thanks for posting this Keith it sounds really interesting. I'm an aural tuner but I am looking at Reyburn Cybertuner and Verituner and would be interested in this as another option. I would really like to hear this on a piano that I could try out in person.

There seems to be a bit of a disconnect here. I doubt that the tuning on this recording would have made the hair on the back of Jurgen's neck stand on end. ( Maybe on the top of his head).

It's too bad the recording is just a bunch of arpeggios I sure wouldn't be checking a tuning out that way if I got to sit down to one of these pianos. I would have liked to hear some long octaves and double octaves and some M3, M10 & M17 progressions. I would have liked to hear some sustained unisons in the mid range. I know from personal experience that a mediocre tuning can sound passable if you just play a bunch of chords and don't linger over the intervals too long.

The top end sounds really flat but I know that I stretch the last octave a more than Tunelab for example, which I have been playing around with. I just can't live with the flat sound and until I start hearing otherwise from my clients, I won't be changing that any time soon. Nice to hear from others on this. The treble stretch sounded off to me.

The spinet sounds really bad but then spinets always do. I would have liked to hear some chromatic octaves around the bass tenor break and some double octaves held long enough to hear how much they wobble.

_________________________
Piano Technicianwww.pianotech.caPiano tuners make the world a better place, one string at a time.

I’m not a tuner-technician nor a physicist, but when I read things like this, I have my doubt about the seriousness of Mr Stooper:

"It is not possible to reach this precision with the usual electronic tuning devices or the usual two-note aural bearing plan techniques. Since the devices jugde the pitch and frequency in the frequency domain, it is necessary, due to the HEISENBERG UNCERTAINITY to analyze the signal over a relative long time. Tuning those three-note octaves and fifths combinations aural to pure state, aural pitch setting is as accurate as tuning unisons aural, what defintitvely does not work with nowadays ETDs."

A rapid search in Wikipedia: "In quantum physics, the Heisenberg uncertainty principle states that the position and momentum of a particle cannot both be known simultaneously. "

What has Heisenberg uncertainty principle to do with piano tuning?

Another example:

"[...] the FRACTAL SYMMETRY of the beat-relations to the interval relations in the “stopper-tuning”. Since due to the extension of the tuning matter FROM TWO DIMENSIONS TO THREE (AND MORE) DIMENSIONS the octaves/fifths problem dissappears, the mighty octave must be asked in place."

He also speaks of supersymmetry...

I would be interested to have the opinion of a physicist/mathematician...

I have had a listen to the audio file, and I can tell you this is not a fair example of this tuning. To really judge this type of mathematical equation, I feel the instrument needed to form a fair opinion, would be something in the 6ft. range or longer. Underneath this, the math scale (on the plate) produces too much error. On the spinet it may not be out of tune unisons, it may be a case of poor string or poor scaling.

As far as running this by a physicist, I would think that they might be able to give you the math on a page or academically, correct or not correct, but with each instrument the math may change slightly according to the attributes or the shortcomings of each instrument. This would be where tuning changes from a science to an art. Each piano is slightly different is very subtle ways. The tuner’s job is to find the “feel” of where the math equation “sounds best” on each and every piano. Sometimes the math has to be abstracted considerably for the sound to line up correctly, especially on small uprights.

Like Thomson I would like to try this temperament out on my own, up close and personal.

Thanks for all the comments about the audio files of tunings done with Bernhard Stopper's software.

I think the tunings are good, but then, since I was the one who did the tunings, I would think that, wouldn't I? 8^)

These were real tunings of real pianos; they were not done under lab conditions. All unisons were open, no mute strips. The recordings were done in the field with an inexpensive digital audio recorder.

There is no perfect tuning among tunings done by someone other than oneself. It is easy to find fault with a tuning when you were not the one who had to work out the compromises.

Not everyone will like these tunings. If you are one who doesn't like the tunings, then don't give another thought to them or to Stopper's software.

However, plenty of people will like the tunings, and for those people, I am reporting a new software tool that is available.

Yes the tuning sounds better on a better piano no doubt about it. Ok, A sharp, D flat and D there is something wrong up top with these. In the top two octaves, I can hear flatness or something,... the circle of fifths is off somewhere. I really need to be there to determine what I am hearing correctly.

The spinet, I didn’t think did the tuning justice, but remember it is a spinet. For me it sounds like a nicely tuned spinet. You can hear the poor tones on that one, mostly poor string, not the tuning. Actually the top of the spinet sounds better than the other two.

I would agree with you about checking the tuning by leaving the strips in. However, I check the “sound of the tuning” by taking an octave and a third, and playing chromatically down or up with all tools removed from the instrument.

There should be a smooth roll increasing slightly all the way up and the reverse going down. Also if you strike 4 C’s or 4 F’s all at once and see how much “wind” there is in the stretch.

I can’t seem to find your mention of other information in the tuning pin thread? I saw the posting earlier last week before you started this thread but no luck in finding it……………….

Hello Kent,

Welcome to this forum. I am an aural tuner only. Do you have a place where I can get the mathematical equation to try this out myself, or is it just for machine tuners?

Piano QC, it would be nice if you spelled the gentleman's name correctly...

Stopper will be the first to tell you that the uniquness of this tuning is so sublte as to not, or hardly, become apparent in short pianos, never mind PSOs like the Everett.

And while he may bring in some references and terms that you or I don't understand, please don't discount him or his work for that. And above all, do not doubt his seriousness, especfially being a non-tech as you are.

Stopper is an extremely bright man. He studied to become a piano builder under one of Germany's foremost master craftsmen piano makers, who accepted only top-notch applicants. He has quite the resume.

In the end, it is the tone and character of the piano that matters. And having heard, felt and experienced it, I am now a believer. Do I use his software? No. I am an aural tuner. But maybe in the very near future that will change.....

I’m just a little bit surprised to find terms like "Supersymmetry" and "Heisenberg uncertainty principle" in Mr. Stopper’s documents as these are terms always used in the context of Quantum Mechanics (theoretical physics) and (to my knowledge) have nothing to do with macroscopic world. But, OF COURSE, I can be wrong. Perhaps Mr. Stopper could explain what he means...

Either way, a piano is either in tune, or out of tune. Whether mean tone, ET tuning, Well Tempered, Stopper tuning or what have you, if the unison's are not correct, the piano is out of tune with either tuning regardless of said tuning.

I discount the Stopper tuning in that regard for this reason. The fact that if you listen to most notes played in the center section, comparing them to most notes played in the upper register, in particular, the utmost highest register, the upper register is actually quite flat of the mid section and, many unison's are out of tune as well.

Now, maybe this is the way this particular tuning is designed to be. This, I do not know. But, I was trained that, either a piano is in tune, or it's not. Which is it? In this case, it is not. Don't take it wrong, I'm not being sarcastic...

Originally posted by PianoQC: I’m not a tuner-technician nor a physicist, but when I read things like this, I have my doubt about the seriousness of Mr Stooper:

"It is not possible to reach this precision with the usual electronic tuning devices or the usual two-note aural bearing plan techniques. Since the devices jugde the pitch and frequency in the frequency domain, it is necessary, due to the HEISENBERG UNCERTAINITY to analyze the signal over a relative long time. Tuning those three-note octaves and fifths combinations aural to pure state, aural pitch setting is as accurate as tuning unisons aural, what defintitvely does not work with nowadays ETDs."

A rapid search in Wikipedia: "In quantum physics, the Heisenberg uncertainty principle states that the position and momentum of a particle cannot both be known simultaneously. "

What has Heisenberg uncertainty principle to do with piano tuning?

Another example:

"[...] the FRACTAL SYMMETRY of the beat-relations to the interval relations in the “stopper-tuning”. Since due to the extension of the tuning matter FROM TWO DIMENSIONS TO THREE (AND MORE) DIMENSIONS the octaves/fifths problem dissappears, the mighty octave must be asked in place."

He also speaks of supersymmetry...

I would be interested to have the opinion of a physicist/mathematician... [/b]

I'm a math student.

Though I'm not an expert in math or physics, I suspect that there's a little fuzziness going on here.

First of all, as you mentioned, the Heisenberg Uncertainty Principle really only applies to material on the quantum level (we can sometimes try to apply quantum mechanics to the real world, but any conclusions we might draw are very negligible). So I'm just as stumped as you are - I have absolutely no idea what this could have to do with piano tuning.

I once read a book called Fractals in Music by Charles Madden. There was quite a bit of discussion on self-similarity, which he describes using the concept of "Cauchy sequence". To illustrate, consider hooking a video camera up to your TV, where the TV displays whatever the camera captures (have you ever done this before?). What if I point the camera toward the TV itself? We can see the TV within a TV, and a TV within that TV; the "sequence" will go on forever, but we will see that eventually, the TV's get arbitrarily close together, almost to the point where the distance between them will vanish. If we were to zoom in further, we will still observe the same configuration. Perhaps this same effect can be seen when you view a mirror with a mirror.

So, Madden talks about how the harmonic series forms a Cauchy sequence. We can see this by examining the series for A-55: 55Hz, 110, 165, 220, 275, 330, etc... If we look at the ratios between a term and its preceding, they are: 2, 1.5, 1.333333..., 1.25, and so on. If we continue, we adjacent terms will get closer and closer to each other (and, actually, this sequence will converge to 1) - we say that this sequence in particular is indeed Cauchy. Given this, we might conclude that the harmonic series is self-similar.

The actual excerpt involves talk of "Fractal Symmetry" and tuning in "higher dimensions". Fractals are very peculiar objects that exhibit self-similarity, a type of symmetry. It could be that "Fractal Symmetry" really means self-similarity. More clarification is needed. And, again, the talk of "higher dimensions" could perhaps refer to techniques in modeling the vibrations of a string, for instance, by using ideas from Linear Algebra to find a (possibly infinite dimensional) vector space to do it. But, this is such a vague statement, and really needs more clarification.

My personal opinion of those excerpts is that they are written to make it appear that there is something very deep (and perhaps intimidating) about this method. So, I wouldn't take it very seriously.

Please let me know if I could perhaps provide more clarification on some of these ideas, or if you have any comments.

His statement about the uncertainty principle was made in reference to his tuning device having to take a longer time to determine the note placement, not the actual note placement. It seems to be an explanation of why his device isn't as fast or something. You are right, it has nothing to do with tuning but the actual physics involved in reading sound waves. Don't get me wrong, I'm not saying that is true, it just appears like that is what he is talking about.

Here is a description of the recordings, so you will know exactly what it is you are trashing -- or appreciating.

I offer an audio recording of a Steinway D and a Bösendorfer Imperial tuned together with Stopper's software. By the way, PureTuner tunes the notes of the scale down to C0, so all 97 of the Bösendorfer's notes can be tuned directly by PureTuner.

My recording attempts to show that each piano is well-tuned with itself and that the pianos also are tuned together quite well. The Steinway plays first and should be on the right. The pianos are side by side. In the recording you hear Steinway arpeggios, then Bösendorfer arpeggios, a Bösendorfer chord of nature progression, a Steinway chord of nature progression, and finally a chromatic scale played on both pianos together.

The recording was not done under "laboratory" conditions; these are real tunings of real pianos; there may be questionable unisons in the high treble, especially on the Bösendorfer. You are welcome to come try to tune them yourself if you think you can do better!

I believe the results that are heard in the recording are good. These results are interesting given how PureTuner was able to accomplish the tunings without taking readings off of either piano in order to calculate a tuning before beginning to tune.

Although the Steinway D and Bösendorfer Imperial have widely disparate scales, and tuning them together is a good demonstration of PureTuner's capabilities, some are wondering how well PureTuner can tune a spinet.

This is an audio recording of the results of a tuning with PureTuner of a Cable-Neson spinet built by Everett. Everett spinets have some of the highest inharmonicity on the planet. The recording follows the form set by the previous Steinway/Bösendorfer recording: arpeggios, chord of nature progression, chromatic filled-in triple octave across entire keyboard, chromatic 12ths across entire keyboard, and finally some chromatic 3rds, 4ths, 5ths, and 6ths in the midrange. I believe the results are good, and as always, PureTuner took no readings from the piano in order to calculate a tuning. One just boots the program, chooses a pitch level, and starts tuning in any order.

Originally posted by Keith Roberts: His statement about the uncertainty principle was made in reference to his tuning device having to take a longer time to determine the note placement, not the actual note placement. It seems to be an explanation of why his device isn't as fast or something. You are right, it has nothing to do with tuning but the actual physics involved in reading sound waves. Don't get me wrong, I'm not saying that is true, it just appears like that is what he is talking about. [/b]

Thanks.

I looked into it a little more, and it does indeed seem that the Heisenberg Uncertainty Principle does have an effect on reading the vibrations of a string. The main result is that the longer you attempt to read the frequency, the easier it will be to determine.

Originally posted by Kent Swafford:...PureTuner took no readings from the piano in order to calculate a tuning. One just boots the program, chooses a pitch level, and starts tuning in any order...

How does this square with the common understanding that the degree of stretch needed for a good tuning depends on the inharmonicity of the strings? With the SAT, CyberTuner, TuneLab, and Verituner, the target pitches are dependent on the inharmonicity of the particular strings in that piano. The first three of these devices take inharmonicity measurements ahead of time, and the Verituner takes measurements as you tune. In exchange, Verituner places some reasonable limitations on the order of tuning. Even purely aural tuning, when measured afterwards, shows the tendancy to make the overall stretch depend on the inharmonicity.

If Stopper's PureTuner software allows tuning in any order without pre-measurements, then supposedly I could start tuning at C8 if I so desired. That means the software would have to already know the target pitch of C8 before any inharmonicity information is available. Whatever that target pitch is, it would have to be the same for a high-inharmonicity piano and a low-inharmonicity piano. Has anyone posted a typical Stopper tuning as measured by, say, a SAT?